A computational fluid-structure interaction analysis of a fiber-reinforced stentless aortic valve

The importance of the aortic root compliance in the aortic valve performance has most frequently been ignored in computational valve modeling, although it has a significant contribution to the functionality of the valve. Aortic root aneurysm or (calcific) stiffening severely affects the aortic valve behavior and, consequently, the cardiovascular regulation. The compromised mechanical and hemodynamical performance of the valve are difficult to study both 'in vivo' and 'in vitro'. Computational analysis of the valve enables a study on system responses that are difficult to obtain otherwise. In this paper a numerical model of a fiber-reinforced stentless aortic valve is presented. In the computational evaluation of its clinical functioning the interaction of the valve with the blood is essential. Hence, the blood-tissue interaction is incorporated in the model using a combined fictitious domain/arbitrary Lagrange-Euler formulation, which is integrated within the Galerkin finite element method. The model can serve as a diagnostic tool for clinical purposes and as a design tool for improving existing valve prostheses or developing new concepts. Structural mechanical and fluid dynamical aspects are analyzed during the systolic course of the cardiac cycle. Results show that aortic root compliance largely influences the valve opening and closing configurations. Stresses in the delicate parts of the leaflets are substantially reduced if fiber-reinforcement is applied and the aortic root is able to expand.     

A design-based model of the aortic valve for fluid-structure interaction

Biomechanics and Modeling in Mechanobiology - This paper presents a new method for modeling the mechanics of the aortic valve and simulates its interaction with blood. As much as possible, the...     

A two-dimensional fluid-structure interaction model of the aortic valve [correction of value

Failure of synthetic heart valves is usually caused by tearing and calcification of the leaflets. Leaflet fiber-reinforcement increases the durability of these valves by unloading the delicate parts of the leaflets, maintaining their physiological functioning. The interaction of the valve with the surrounding fluid is essential when analyzing its functioning. However, the large differences in material properties of fluid and structure and the finite motion of the leaflets complicate blood-valve interaction modeling. This has, so far, obstructed numerical analyses of valves operating under physiological conditions. A two-dimensional fluid-structure interaction model is presented, which allows the Reynolds number to be within the physiological range, using a fictitious domain method based on Lagrange multipliers to couple the two phases. The extension to the three-dimensional case is straightforward. The model has been validated experimentally using laser Doppler anemometry for measuring the fluid flow and digitized high-speed video recordings to visualize the leaflet motion in corresponding geometries. Results show that both the fluid and leaflet behaviour are well predicted for different leaflet thicknesses.     

An approach to the simulation of fluid-structure interaction in the aortic valve

A pair of finite element models has been employed to study the interaction of blood flow with the operation of the aortic valve. A three-dimensional model of the left ventricle with applied wall displacements has been used to generate data for the spatially and time-varying blood velocity profile across the aortic aperture. These data have been used as the inlet loading conditions in a three-dimensional model of the aortic valve and its surrounding structures. Both models involve fluid-structure interaction and simulate the cardiac cycle as a dynamic event. Confidence in the models was obtained by comparison with data obtained in a pulse duplicator. The results show a circulatory flow being generated in the ventricle which produces a substantially axial flow through the aortic aperture. The aortic valve behaves in an essentially symmetric way under the action of this flow, so that the pressure difference across the leaflets is approximately uniform. This work supports the use of spatially uniform but temporally variable pressure distributions across the leaflets in dry or structural models of aortic valves. The study is a major advance through its use of truly three-dimensional geometry, spatially non-uniform loading conditions for the valve leaflets and the successful modelling of progressive contact of the leaflets in a fluid environment.     

A fully coupled fluid-structure interaction model of the secondary lymphatic valve

Abstract

The secondary lymphatic valve is a bi-leaflet structure frequent throughout collecting vessels that serves to prevent retrograde flow of lymph. Despite its vital function in lymph flow and apparent importance in disease development, the lymphatic valve and its associated fluid dynamics have been largely understudied. The goal of this work was to construct a physiologically relevant computational model of an idealized rat mesenteric lymphatic valve using fully coupled fluid-structure interactions to investigate the relationship between three-dimensional flow patterns and stress/deformation within the valve leaflets. The minimum valve resistance to flow, which has been shown to be an important parameter in effective lymphatic pumping, was computed as 268?g/mm⁴?s. Hysteretic behavior of the lymphatic valve was confirmed by comparing resistance values for a given transvalvular pressure drop during opening and closing. Furthermore, eddy structures were present within the sinus adjacent to the valve leaflets in what appear to be areas of vortical flow; the eddy structures were characterized by non-zero velocity values (up to ～4?mm/s) in response to an applied unsteady transvalvular pressure. These modeling capabilities present a useful platform for investigating the complex interplay between soft tissue motion and fluid dynamics of lymphatic valves and contribute to the breadth of knowledge regarding the importance of biomechanics in lymphatic system function.     

A three-dimensional mechanical analysis of a stentless fibre-reinforced aortic valve prosthesis

Failure of bioprosthetic and synthetic three-leaflet valves has been shown to occur as a consequence of high tensile and bending stresses, acting on the leaflets during opening and closing. Moreover, in the stented prostheses, whether synthetic or biological, the absence of contraction of the aortic base, due to the rigid stent, causes the leaflets to be subjected to an unphysiological degree of flexure, which is related to calcification. It is shown that the absence of the stent, which gives a flexible aortic base and leaflet attachment, and leaflet fibre-reinforcement result in reduced stresses in the weaker parts of the leaflets in their closed configuration. It is postulated that this leads to a decrease of tears and perforations, which may result in a improved long-term behaviour. The effect of a flexible leaflet attachment and aortic base of a synthetic valve is investigated with a finite element model. Different fibre-reinforced structures are analysed with respect to the stresses that are likely to contribute to the failure of fibre-reinforced prostheses and compared with the results obtained for a stented prosthesis. Results show that for the stentless models a reduction of stresses up to 75% is obtained with respect to stented models with the same type of reinforcement.     

Three-dimensional computational model of left heart diastolic function with fluid-structure interaction

Aided by advancements in computer speed and modeling techniques, computational modeling of cardiac function has continued to develop over the past twenty years. The goal of the current study was to develop a computational model that provides blood-tissue interaction under physiologic flow conditions, and apply it to a thin-walled model of the left heart. To accomplish this goal, the Immersed Boundary Method was used to study the interaction of the tissue and blood in response to fluid forces and changes in tissue pathophysiology. The fluid mass and momentum conservation equations were solved using Patankar's Semi-Implicit Method for Pressure Linked Equations (SIMPLE). A left heart model was developed to examine diastolic function, and consisted of the left ventricle, left atrium, and pulmonary flow. The input functions for the model included the pulmonary driving pressure and time-dependent relationship for changes in chamber tissue properties during the simulation. The results obtained from the left heart model were compared to clinically observed diastolic flow conditions for validation. The inflow velocities through the mitral valve corresponded with clinical values (E-wave = 74.4 cm/s, A-wave = 43 cm/s, and E/A = 1.73). The pressure traces for the atrium and ventricle, and the appearance of the ventricular flow fields throughout filling, agreed with those observed in the heart. In addition, the atrial flow fields could be observed in this model and showed the conduit and pump functions that current theory suggests. The ability to examine atrial function in the present model is something not described previously in computational simulations of cardiac function.     

Wall stress and flow dynamics in abdominal aortic aneurysms: finite element analysis vs. fluid-structure interaction

Abdominal aortic aneurysm (AAA) rupture is the clinical manifestation of an induced force exceeding the resistance provided by the strength of the arterial wall. This force is most frequently assumed to be the product of a uniform luminal pressure acting along the diseased wall. However fluid dynamics is a known contributor to the pathogenesis of AAAs, and the dynamic interaction of blood flow and the arterial wall represents the in vivo environment at the macro-scale. The primary objective of this investigation is to assess the significance of assuming an arbitrary estimated peak fluid pressure inside the aneurysm sac for the evaluation of AAA wall mechanics, as compared with the non-uniform pressure resulting from a coupled fluid-structure interaction (FSI) analysis. In addition, a finite element approach is utilised to estimate the effects of asymmetry and wall thickness on the wall stress and fluid dynamics of ten idealised AAA models and one non-aneurysmal control. Five degrees of asymmetry with uniform and variable wall thickness are used. Each was modelled under a static pressure-deformation analysis, as well as a transient FSI. The results show that the inclusion of fluid flow yields a maximum AAA wall stress up to 20% higher compared to that obtained with a static wall stress analysis with an assumed peak luminal pressure of 117 mmHg. The variable wall models have a maximum wall stress nearly four times that of a uniform wall thickness, and also increasing with asymmetry in both instances. The inclusion of an axial stretch and external pressure to the computational domain decreases the wall stress by 17%.     

Numerical simulation of two-phase non-Newtonian blood flow with fluid-structure interaction in aortic dissection

The behavior of blood cells and vessel compliance significantly influence hemodynamic parameters, which are closely related to the development of aortic dissection. Here the two-phase non-Newtonian model and the fluid-structure interaction (FSI) method are coupled to simulate blood flow in a patient-specific dissected aorta. Moreover, three-element Windkessel model is applied to reproduce physiological pressure waves. Important hemodynamic indicators, such as the spatial distribution of red blood cells (RBCs) and vessel wall displacement, which greatly influence the hemodynamic characteristics are analyzed. Results show that the proximal false lumen near the entry tear appears to be a vortex zone with a relatively lower volume fraction of RBCs, a low time-averaged wall shear stress (TAWSS) and a high oscillatory shear index (OSI), providing a suitable physical environment for the formation of atherosclerosis. The highest TAWSS is located in the narrow area of the distal true lumen which might cause further dilation. TAWSS distributions in the FSI model and the rigid wall model show similar trend, while there is a significant difference for the OSI distributions. We suggest that an integrated model is essential to simulate blood flow in a more realistic physiological environment with the ultimate aim of guiding clinical treatment.     

Validation of a fluid-structure interaction model of a heart valve using the dynamic mesh method in fluent

Simulations of coupled problems such as fluid-structure interaction (FSI) are becoming more and more important for engineering purposes. This is particularly true when modeling the aortic valve, where the FSI between the blood and the valve determines the valve movement and the valvular hemodynamics. Nevertheless only a few studies are focusing on the opening and closing behavior during the ejection phase (systole). In this paper, we present the validation of a FSI model using the dynamic mesh method of Fluent for the two-dimensional (2D) simulation of mechanical heart valves during the ejection phase of the cardiac cycle. The FSI model is successfully validated by comparing simulation results to experimental data obtained from in vitro studies using a CCD camera.     

Validation of a 3D computational fluid-structure interaction model simulating flow through an elastic aperture

This work presents a validation of a fluid-structure interaction computational model simulating the flow conditions in an in vitro mock heart chamber modeling mitral valve regurgitation during the ejection phase during which the trans-valvular pressure drop and valve displacement are not as large. The mock heart chamber was developed to study the use of 2D and 3D color Doppler techniques in imaging the clinically relevant complex intra-cardiac flow events associated with mitral regurgitation. Computational models are expected to play an important role in supporting, refining, and reinforcing the emerging 3D echocardiographic applications. We have developed a 3D computational fluid-structure interaction algorithm based on a semi-implicit, monolithic method, combined with an arbitrary Lagrangian-Eulerian approach to capture the fluid domain motion. The mock regurgitant mitral valve corresponding to an elastic plate with a geometric orifice, was modeled using 3D elasticity, while the blood flow was modeled using the 3D Navier-Stokes equations for an incompressible, viscous fluid. The two are coupled via the kinematic and dynamic conditions describing the two-way coupling. The pressure, the flow rate, and orifice plate displacement were measured and compared with numerical simulation results. In-line flow meter was used to measure the flow, pressure transducers were used to measure the pressure, and a Doppler method developed by one of the authors was used to measure the axial displacement of the orifice plate. The maximum recorded difference between experiment and numerical simulation for the flow rate was 4%, the pressure 3.6%, and for the orifice displacement 15%, showing excellent agreement between the two.     

Numerical simulation of the dynamics of a bileaflet prosthetic heart valve using a fluid-structure interaction approach

The main purpose of this study is to reproduce in silico the dynamics of a bileaflet mechanical heart valve (MHV; St Jude Hemodynamic Plus, 27mm characteristic size) by means of a fully implicit fluid-structure interaction (FSI) method, and experimentally validate the results using an ultrafast cinematographic technique. The computational model was constructed to realistically reproduce the boundary condition (72 beats per minute (bpm), cardiac output 4.5l/min) and the geometry of the experimental setup, including the valve housing and the hinge configuration. The simulation was carried out coupling a commercial computational fluid dynamics (CFD) package based on finite-volume method with user-defined code for solving the structural domain, and exploiting the parallel performance of the whole numerical setup. Outputs are leaflets excursion from opening to closure and the fluid dynamics through the valve. Results put in evidence a favorable comparison between the computed and the experimental data: the model captures the main features of the leaflet motion during the systole. The use of parallel computing drastically limited the computational costs, showing a linear scaling on 16 processors (despite the massive use of user-defined subroutines to manage the FSI process). The favorable agreement obtained between in vitro and in silico results of the leaflet displacements confirms the consistency of the numerical method used, and candidates the application of FSI models to become a major tool to optimize the MHV design and eventually provides useful information to surgeons.     

A novel heart valve stent design: mechanical interaction with the aortic root

Percutaneous aortic valve implantation has become an alternative technique to surgical valve replacement in patients with high risk for open chest surgery. Vascular stents clinically used today for non-invasive aortic valve replacement tend, however, to impede the dimension changes of the compliant aortic root over the cardiac cycle. The purpose of the present work is to assess the influence of a novel heart valve stent, designed specifically to limit the traumatism in tissue, on the compliance of the aortic root. A theoretical approach is adopted to model the mechanical behaviour of the different stent parts and assess the compliance modification induced by the stent. The validity of the model is then tested experimentally. Both approaches show that the specific geometry of the stent makes it possible to keep the compliance of the aortic root close to the native root values.     

Patient-specific modeling of biomechanical interaction in transcatheter aortic valve deployment

The objective of this study was to develop a patient-specific computational model to quantify the biomechanical interaction between the transcatheter aortic valve (TAV) stent and the stenotic aortic valve during TAV intervention. Finite element models of a patient-specific stenotic aortic valve were reconstructed from multi-slice computed tomography (MSCT) scans, and TAV stent deployment into the aortic root was simulated. Three initial aortic root geometries of this patient were analyzed: (a) aortic root geometry directly reconstructed from MSCT scans, (b) aortic root geometry at the rapid right ventricle pacing phase, and (c) aortic root geometry with surrounding myocardial tissue. The simulation results demonstrated that stress, strain, and contact forces of the aortic root model directly reconstructed from MSCT scans were significantly lower than those of the model at the rapid ventricular pacing phase. Moreover, the presence of surrounding myocardium slightly increased the mechanical responses. Peak stresses and strains were observed around the calcified regions in the leaflets, suggesting the calcified leaflets helped secure the stent in position. In addition, these elevated stresses induced during TAV stent deployment indicated a possibility of tissue tearing and breakdown of calcium deposits, which might lead to an increased risk of stroke. The potential of paravalvular leak and occlusion of coronary ostia can be evaluated from simulated post-deployment aortic root geometries. The developed computational models could be a valuable tool for pre-operative planning of TAV intervention and facilitate next generation TAV device design.     

Multi-modality image-based computational analysis of haemodynamics in aortic dissection

Aortic dissection is a disease whereby an injury in the wall of the aorta leads to the creation of a true lumen and a false lumen separated by an intimal flap which may contain multiple communicating tears between the lumina. It has a high associated morbidity and mortality, but at present, the timing of surgical intervention for stable type B dissections remains an area of debate. Detailed knowledge of haemodynamics may yield greater insight into the long-term outcomes for dissection patients by providing a greater understanding of pressures, wall shear stress and velocities in and around the dissection. In this paper, we aim to gather further insight into the complex haemodynamics in aortic dissection using medical imaging and computational fluid dynamics modelling. Towards this end, several computer models of the aorta of a patient presenting with an acute Stanford type B dissection were created whereby morphometric parameters related to the dissection septum were altered, such as removal of the septum, and the variation of the number of connecting tears between the lumina. Patient-specific flow data acquired using 2D PC-MRI in the ascending aorta were used to set the inflow boundary condition. Coupled zero-dimensional (Windkessel) models representing the distal vasculature were used to define the outlet boundary conditions and tuned to match 2D PC-MRI flow data acquired in the descending aorta. Haemodynamics in the dissected aorta were compared to those in an equivalent ‘healthy aorta’, created by virtually removing the intimal flap (septum). Local regions of increased velocity, pressure, wall shear stress and alterations in flow distribution were noted, particularly in the narrow true lumen and around the primary entry tear. The computed flow patterns compared favourably with those obtained using 4D PC-MRI. A lumped-parameter heart model was subsequently used to show that in this case there was an estimated 14 % increase in left ventricular stroke work with the onset of dissection. Finally, the effect of secondary connecting tears (i.e. those excluding the primary entry and exit tears) was also studied, revealing significant haemodynamic changes when no secondary tears are included in the model, particularly in the true lumen where increases in flow over \(+200\,\%\) and drops in peak pressure of 18 % were observed.     

Postoperative analysis of the mechanical interaction between stent and host tissue in patients after transcatheter aortic valve implantation

The analysis is based on a finite element procedure to extract the contact forces between an implanted Nitinol stent and the surrounding host tissue using postoperative CT images. The methodology was applied for patients (N=46) which have undergone a TAVI procedure with the Medtronic CoreValve Revalving System (MCRS) to obtain corresponding deformation and force maps. The postoperative CT data were recorded for each patient in both systolic and diastolic phase of the heart cycle. Scalar parameters were defined, which map deformed geometry and contact force field to mechanically relevant quantities: radial dilatation, radial shape distortion, non-convex points, mean force, a force deviation measure and a pressure equivalent. The latter demonstrates that in the area of the aortic root, the added circumferential loading is of the same order as the baseline average blood pressure, thus leading to a doubling of the local mechanical load. Generally the force distribution along the stent is non-homogeneous. A comparison of systolic and diastolic data revealed slightly higher contact forces during the diastole, indicating that the stent has to carry more load in this phase. The geometrical and mechanical parameters were compared for two types of clinical complication: para-valvular leakage (PVL) and permanent pacemaker requirement (PPM). It was found that an increase in mean force can be associated with both complications; significantly for PVL and as a trend for PPM.     

Haemodynamics and stresses in abdominal aortic aneurysms: A fluid-structure interaction study into the effect of proximal neck and iliac bifurcation angle

Our knowledge of how geometry influences abdominal aortic aneurysm (AAA) biomechanics is still developing. Both iliac bifurcation angle and proximal neck angle could impact the haemodynamics and stresses within AAA. Recent comparisons of the morphology of ruptured and intact AAA show that cases with large iliac bifurcation angles are less likely to rupture than those with smaller angles. We aimed to perform fluid-structure interaction (FSI) simulations on a range of idealised AAA geometries to conclusively determine the influence of proximal neck and iliac bifurcation angle on AAA wall stress and haemodynamics.Peak wall shear stress (WSS) and time-averaged WSS (TAWSS) in the AAA sac region only increased when the proximal neck angle exceeded 30°. Both peak WSS (p < 0.0001) and peak von Mises wall stress (p = 0.027) increased with iliac bifurcation angle, whereas endothelial cell activation potential (ECAP) decreased with iliac bifurcation angle (p < 0.001) and increased with increasing neck angle.These observations may be important as AAAs have been shown to expand, develop thrombus and rupture in areas of low WSS. Here we show that AAAs with larger iliac bifurcation angles have higher WSS, potentially reducing the likelihood of rupture. Furthermore, ECAP was lower in AAA geometries with larger iliac bifurcation angles, implying less likelihood of thrombus development and wall degeneration. Therefore our findings could help explain the clinical observation of lower rupture rates associated with AAAs with large iliac bifurcation angles.     

New insights into the assessment of the prosthetic valve performance in the presence of subaortic stenosis through a fluid-structure interaction model

The aim of this study was to contribute to improving the accuracy of clinical assessments of valve performance in situations involving the concomitant presence of a prosthetic valve and subaortic stenosis (SAS). Physiological flow in a two-dimensional model for a bileaflet mechanical heart valve was investigated numerically in terms of the fluid-structure interactions. The fluid dynamics in a model with SAS of the left ventricle outflow tract were compared with those given by a healthy model. The results show that in the model with SAS, one leaflet did not close during the observed systolic phase, whereas the other one showed similar behaviour to that of the leaflet in the healthy model. In addition, the main flow did not occur along the central axis and a deviated jet was set up between leaflets, contrary to what occurred in the model without SAS. Current clinical diagnostic indices, which are mainly based on the central jet flow velocities, are therefore unsuitable for use in this pathological situation and should be used with great caution.     

A distributed lumped parameter model of blood flow with fluid-structure interaction

Biomechanics and Modeling in Mechanobiology - A distributed lumped parameter (DLP) model of blood flow was recently developed that can be simulated in minutes while still incorporating complex...